Saving a character so it can be opened in a seperate blender project
File/Link or File/Append will be useful.

Save your character as a .blend file.  From the "set" file use the menu option File/Append or File/Link. You will get the best results when when Append or Link from one .blend file to another .blend file.  File/Append ... File/Append is a great way to reuse and asset and animation across files.  Linked Libraries.  Link below.

The blender terminology for this is File/Append or File/Link.  Import is probably not what you want.

When you File/Append ... Choose the object or Mesh or Armature or Group.  You will travel through a hierarchy  to find what you need. Blender will also link/append related items.  You can design Groups to be linked/appended.  

See this link.
http://wiki.blender.org/index.php/Doc:2.6/Manual/Data_System/Linked_Libraries